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Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations, N.V. Krylov


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Автор: N.V. Krylov
Название:  Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
ISBN: 9781470447403
Издательство: Mare Nostrum (Eurospan)
Классификация:


ISBN-10: 1470447401
Обложка/Формат: Hardback
Страницы: 456
Вес: 0.52 кг.
Дата издания: 30.09.2018
Серия: Mathematical surveys and monographs
Язык: English
Размер: 254 x 178
Читательская аудитория: Professional and scholarly
Ключевые слова: Differential calculus & equations,Applied mathematics
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Поставляется из: Англии
Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrovs elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lins like estimates, and on the so-called ``ersatz existence theorems, saying that one can slightly modify ``any equation and get a ``cut-off equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
Дополнительное описание: Differential calculus and equations|Applied mathematics


Nonlinear parabolic and elliptic equations

Автор: Pao, C. V.
Название: Nonlinear parabolic and elliptic equations
ISBN: 1461363233 ISBN-13(EAN): 9781461363231
Издательство: Springer
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Цена: 158380.00 T
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Описание: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Elliptic and Parabolic Equations

Автор: Joachim Escher; Elmar Schrohe; J?rg Seiler; Christ
Название: Elliptic and Parabolic Equations
ISBN: 3319381504 ISBN-13(EAN): 9783319381503
Издательство: Springer
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Цена: 102480.00 T
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Описание: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations.

Elliptic and Parabolic Equations

Автор: Joachim Escher; Elmar Schrohe; J?rg Seiler; Christ
Название: Elliptic and Parabolic Equations
ISBN: 331912546X ISBN-13(EAN): 9783319125466
Издательство: Springer
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Цена: 130430.00 T
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Описание: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations.

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

Автор: J?rgen Fuhrmann; Mario Ohlberger; Christian Rohde
Название: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems
ISBN: 3319055909 ISBN-13(EAN): 9783319055909
Издательство: Springer
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Цена: 149060.00 T
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Описание: The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications.

Geometric Properties for Parabolic and Elliptic PDE`s

Автор: Rolando Magnanini; Shigeru Sakaguchi; Angelo Alvin
Название: Geometric Properties for Parabolic and Elliptic PDE`s
ISBN: 8847056128 ISBN-13(EAN): 9788847056121
Издательство: Springer
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Цена: 111790.00 T
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Описание: This inclusive study of projective geometry covers analytic and synthetic methods, takes in linear, quadratic, cubic and quartic figures in various dimensions, and deals at length with refinements of basic theories, including those of Pappus and Desargues.

Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems

Автор: Cl?ment Canc?s; Pascal Omnes
Название: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems
ISBN: 3319573934 ISBN-13(EAN): 9783319573939
Издательство: Springer
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Цена: 158380.00 T
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Описание:

This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics.

The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.

The book is useful for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.


Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

Автор: J?rgen Fuhrmann; Mario Ohlberger; Christian Rohde
Название: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems
ISBN: 3319382888 ISBN-13(EAN): 9783319382883
Издательство: Springer
Рейтинг:
Цена: 111790.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications.

Singular Solutions of Nonlinear Elliptic and Parabolic Equations

Автор: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov
Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations
ISBN: 3110315483 ISBN-13(EAN): 9783110315486
Издательство: Walter de Gruyter
Цена: 223090.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography


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